1. Field of the Invention
The present invention relates to a method for simulating fluid flows within a reservoir from methods referred to as chimera methods; which is an alternative solution for reservoir simulation, allowing accounting for the radial directions of flow around wells and thus improving the calculation accuracy. Furthermore, this modular approach allows testing in an efficient and interactive way several development scenarios during modelling.
2. Description of the Prior Art
An oil reservoir is a porous and permeable subsoil formation associated with an impermeable cover that traps hydrocarbons. The order of magnitude of the lateral extension of a reservoir is one kilometer whereas the depth thereof is rather about ten meters. It is crossed by a variable number of geometric discontinuities such as wells or faults.
In oil exploration, survey of an oil reservoir requires simulation of the fluid flows within the reservoir and of the geometric discontinuities running therethrough in order to define the economic interest and the production modes of the field. These simulations are referred to as “reservoir simulations”.
It is therefore necessary to simulate fluid flows over the entire domain covered by the reservoir, by taking into account all the geometric discontinuities running therethrough. The simulation domain is then defined as the set of the reservoir and the geometric discontinuities. This simulation requires, on the one hand, physical modelling of the flows by a set of equations referred to as flow model and, on the other hand, discretization of these equations to solve the problem in an approximate way. The simulation domain is represented by means of a grid allowing discretization of the domain in space, thus allowing solution of the discrete equations and to provide an approximation of the physical solution. Simulation of fluid flows within a reservoir therefore requires two stages:
discretizing the structure of the domain by means of a grid, and
discretizing the flow equations according to the grid selected.
Grid generation is a crucial element for new-generation oil reservoir simulators. A grid allows description of the geometry of the geologic structure studied by means of a representation in discrete elements wherein the simulation is carried out. Better understanding of the physical phenomena involved requires 3D simulation of the multiphase flows in increasingly complex geologic structures, in the neighborhood of different types of singularities such as stratifications, faults, onlaps, channels and complex wells. All this complexity has to be taken into account first by the grid that has to reproduce as accurately as possible the geologic information in its heterogeneous character. Furthermore, good apprehension of the physical phenomena occurring in these complex structures requires a hierarchical and modular grid approach.
The following documents mentioned in the course of the description hereafter illustrate the state of the art:
Alexander S. Williamson and John E. Chappelear, “Representing Wells in Numerical Reservoir Simulation: Part 1 Theory”, SPE 7697, 1981
Sophie Balaven-Clermidy, “Génération de Maillages Hybrides Pour la Modélsation de Réservoirs Pétroliers”, Thèse de doctorat, IFP, Ecole des mines de Paris, 2001.
Chesshire et Henshaw, “Composite Overlapping Meshes for the Solution of Partial Differential Equations”, Journal of Computational Physics 90, 1-64, 1990.
Shih, “Overset grids: Fundamentals and Practical Issues”, AIAA Applied Aerodynamics Conference. 3259, 2002.
Lin, C. W., Smith, G. D., and Fisher, S. C.—Application of a Multiblock Grid Generation Approach to Ship Configuration, 3rd International Conference on Numerical Grid Generation in CFD, Spain, June 1991.
Wells are generally thin tubes having a radius of about ten centimeters and comprising several perforations (at the most permeable points). Scale problems in reservoir modelling are therefore flagrant: the reservoir/well flow models can therefore only be coupled models. This scale difference also has to be taken into account if the discontinuity is a fault, which is why it is crucial to obtain a fine description of the flows around the discontinuities.
There are several known approaches based on the use of a complete grid representing all of the simulation domain (reservoir+discontinuities). A commonly used method consists in gridding the reservoir part of the domain in a single block (several in case of faults) and to integrate the presence of other discontinuities such as wells in the equations. The presence of wells is considered as a source term defined by means of a productivity index Ip. This method is for example described in the document by Williamson (1981).
However, the necessity for a finer description of the flows around discontinuities such as wells leads to the elaboration of a modular approach where the various objects (reservoir and well for example) considered can be taken into account individually. Flow modelling around wells for example is carried out by means of the “well models”. These models allow simulation of multiphase flows in the well drainage area by adopting a small-scale description of the characteristics of the porous medium in the area around the well where the flows are fast.
Thus, in a more recent method developed by the assignee, the reservoir, in the area close to the discontinuity are gridded and the two grids are combined by creating a transition zone. The result is referred to as hybrid grid, as described in the document by S. Balaven-Clermidy (2001).
This method requires a considerable effort for generating the grid of the transition zone notably in three dimensions.
An alternative to this approach is the use of multi-block grids wherein the calculation domain is represented by a set of subdomains, gridded independently of one another. They can overlap one another or not. There are for example multi-block grids with non-coincident overlaps referred to as “chimera grids” or “Composite Overlapping Meshes”. This type of grid is described for example by Chesshire and Henshaw (1990). These chimera grids have been used for about ten years in the field of aeronautics (Shih, 2002) and hydrodynamics (Lin, Smith, G. D., and Fisher (1991) for complex geometries and in particular those with mobile bodies (missiles, helicopter blades, fluid structure coupling, . . . ). This type of grid allows adequate description of the flows on the border of discontinuities, but control of the subdomains regarding flows requires particular methods called chimera methods. However, the current chimera grid creation techniques and the associated chimera methods are not applied for reservoir simulation.